Here is a chart showing the consistency strength and implicational relationships among the large cardinals between supercompact and almost-huge. This is a summary of many of the ideas from chapter two of my dissertation, and it is adapted from a chart appearing in that chapter.
UPDATED June 2014 to reflect my work with Lubarsky on extendible, hypercompact, and enhanced supercompact cardinals.
Norman, it’s a great chart! I do hope we’ll get all these large cardinal notions into Cantor’s Attic!(http://cantorsattic.info)
Next step: we need to convince Victoria Gitman to get her similar chart of the large cardinal hierarchy in the vicinity of Ramsey cardinals also up on Boolesrings. (Vika, are you reading this?)